The reason you cannot see a person standing on the other side of a boundary wall but can hear them is based on the difference in the wavelengths of light and sound.
Light waves have very small wavelengths, in the order of nanometers (approximately \(10^{-9}\) m). These small wavelengths cannot bend around large obstacles like walls, which are much larger than the wavelength of light. As a result, light waves cast sharp shadows, and you cannot see the person standing behind the wall.
Sound waves, on the other hand, have much longer wavelengths, typically in the order of centimeters to meters. These longer wavelengths can diffract around the edges of a boundary, such as a wall, and thus can be heard even though the person is not visible.
This phenomenon is an example of diffraction, where waves spread out and bend around obstacles.
A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find \( \frac{dS}{dx} \).
